High pressure and tide height

It was a spring tide so the water level was going to be low anyway but we were warned to be back to the harbour on time for the boat because high pressure was making the tide even lower. I suppose that it makes sense that if the air pressure is high it will push down more on the sea and lower the level. https://noc.ac.uk/files/documents/business/Tides-and-Meteorological-Effects.pdf has a summary. The effects are spread out over an area but it is true.